The collaboration will hold a VIRTUAL meeting on 11-15 January, 2021, entitled “Donaldson-Thomas invariants and Resurgence”.

Scientific Organizers:
Dominic Joyce, Simon Salamon, and Sakura Schafer-Nameki.

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Summary:
3-Calabi-Yau triangulated categories T are a major area of research in Geometry and String Theory. Examples include derived categories D^bcoh X of coherent sheaves and the derived Fukaya category D^bF(X) on a Calabi-Yau 3-fold X, where Kontsevich’s Homological Mirror Symmetry Conjecture explains mirror symmetry between Calabi-Yau 3-folds X, X* as equivalences of categories D^bcoh X = D^bF(X*), D^bF(X) = D^bcoh X*.

For such a 3-Calabi-Yau category T one can consider the moduli space Stab(T) of Bridgeland stability conditions on T, and for each σ in Stab(T) one can (under good conditions) define Donaldson-Thomas (D-T) invariants DT_α(σ), which are rational numbers ‘counting’ σ-semistable objects in class α in K^num(T).

A nice example, which will be covered at the conference, is a class of categories T of derived representations of a quiver with superpotential (Q,W), in which Stab(T) and DT_α(σ) can be described by work of Bridgeland and Smith in terms of quadratic differentials on a Riemann surface.

Recent work of Tom Bridgeland and coauthors explains how to encode D-T invariants into interesting geometric structures on Stab(T), involving Stokes phenomena and Riemann-Hilbert problems for singular flat connections, and connected (via Tom’s paper with Ian Strachan) to complex hyperkahler manifolds and twistor theory. All this is related to work of Kontsevich and Soibelman on analytic stability data and resurgence, and to a circle of ideas in String Theory, including work of Gaiotto, Moore and Neitzke, and topics such as resurgence, WKB analysis, and line operators.

The conference will explain these ideas with introductory talks, and aim to promote communication between Geometers and String Theorists, to better understand this new and fast-moving area.

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The virtual meeting comes in two parts:

1. Recorded lectures which can be viewed by participants at any time, and;
2. “Live” lectures streamed via Zoom and YouTube, which can also be watched later. Our live sessions will also include some discussions, which may include discussions of both the live lectures and the recorded lectures. YouTube access for the lectures is available at
   https://www.youtube.com/channel/UCGw1y7VGRYGM7Wtk07JtFcA/

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Our recorded lectures are as follows. Those who are unfamiliar with Bridgeland stability should endeavor to watch these recorded lectures before the live lectures by Bridgeland.

• Fabian Haiden (Oxford), Introduction to Bridgeland stability
• Dominic Joyce (Oxford), Donaldson-Thomas theory of Calabi-Yau 3-folds

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Our live schedule is as follows. – All times are given in British time, in honor of the originally planned venue for the meeting, as well as in Eastern Daylight Time. (Please refer to a time zone converter if you aren’t sure what time it will be in your time zone). There will be a brief conference introduction from Robert Bryant prior to the first talk on Monday.

You can download the programme of this meeting, or consult the version below.

Timetable

	MON 11 JANUARY	TUE 12 JANUARY	WED 13 JANUARY	THU 14 JANUARY	FRI 15 JANUARY
16:00-17:00 (GMT) 11:00-12:00 (EST)	B. Pym	M. Kontsevich	G. Moore	T. Bridgeland, III	I.-A. Coman
17:00-17:30 (GMT) 12:00-12:30 (EST)	Questions/Break	Questions/Break	Questions/Break	Questions/Break	Questions/Break
17:30-18:30 (GMT) 12:30-13:30 (EST)	T. Bridgeland, I	M. Mariño	F. Yan	S. Donaldson I	S. Donaldson II
18:45-20:00 (GMT) 13:45-15:00 (EST)	Meal break	Meal break	Meal break	Meal break	Meal break
20:00-21:00 (GMT) 15:00-16:00 (EST)	I. Smith	T. Bridgeland, II	Discussion, led by Maxim Kontsevich and Richard Thomas	Discussion on “complex hyperkähler manifolds”, led by Roger Bielawski	Discussion on “DT invariants and resurgence: Good questions for the future?”, led by Joerg Teschner
21:00-21:30 (GMT) 16:00-16:30 (EST)	Questions/Discussion	Questions/Discussion	Discussion, con.	Discussion, con.	Discussion, con.

Wednesday’s discussion:

Documents associated with Thursday’s discussion:

Slides from Lionel Mason

Documents associated with Friday’s discussion:

Questions from Greg Moore

Speakers:

The links will take you to abstracts, slides of lectures, and/or video recordings of the lectures (when available).

• Tom Bridgeland (Sheffield), From Donaldson-Thomas invariants to complex hyperkahler structures (3 lectures)
• Ioana-Alexandra Coman (Amsterdam), Geometric description of topological string partition functions from quantum curves and integrability
• Simon Donaldson (SCGP and Imperial College London), Deformations of singular sets and Nash-Moser theory I, II
• Maxim Kontsevich (IHES, Paris), Analyticity and resurgence
• Marcos Mariño (Geneva), From resurgence to topological strings
• Greg Moore (Rutgers), Informal Remarks Complementary To, And Preparatory For,
  Fei Yan’s Talk
• Andy Neitzke (Yale), Riemann-Hilbert problems, Hitchin systems and the conformal limit
  Lecture cancelled
• Brent Pym (McGill), Introduction to Stokes phenomena and resurgence
• Ivan Smith (Cambridge), Quadratic differentials as stability conditions
• Fei Yan (Rutgers), Line defects, UV-IR map and exact WKB

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The collaboration co-sponsored a workshop with the American Institute of Mathematics (AIM) on Special Holonomy and Branes on October 26-30 2020. The workshop was organized by Sergei Gukov, Rafe Mazzeo, and Sakura Schafer-Nameki.
The workshop featured extensive discussions as well as lectures; we have preserved the lectures on this website. The entire conference was held online.

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The lecture schedule was as follows. (All times are given in California time.)

Timetable:

	MON 26 OCTOBER	TUE 27 OCTOBER	WED 28 OCTOBER	THU 29 OCTOBER	FRI 30 OCTOBER
08:00-09:30 (PDT)	L. Anderson/ A. Braun	L. Fredrickson/ D. Pei	L. Foscolo	C. Lawrie	T. Walpuski
12:30-14:00 (PDT)	D. Morrison/ J. Lotay	A. Haydys/ J. Sparks	R. Barbosa

Speakers:

The links will take you to abstracts, slides of lectures, and/or video recordings of the lectures (when available).

• Lara Anderson (Virginia Tech), Higgs Bundles in String Compactifications
• Rodrigo Barbosa (Simons Center for Geometry and Physics, Stony Brook), Coassociative ALE Fibrations and Spectral Covers of Riemannian Higgs Bundles
• Andreas Braun (Durham University), Higgs Bundles & Exceptional Holonomy
• Lorenzo Foscolo (University College London), QALF hyperkähler spaces
• Laura Fredrickson (University of Oregon), Branes in the moduli spaces of Higgs bundles, I
• Andriy Haydys (University of Freiburg), Special Kähler and related geometries
• Craig Lawrie (University of Pennsylvania), G2, Spin(7) BPS Equations and T-branes
• Jason D. Lotay (Oxford University), Special holonomy and branes: observations and themes
• David R. Morrison (UC Santa Barbara), Nonabelian Gauge Symmetry in String Theory and its Cousins, including an Introduction to Branes
• Du Pei (Harvard University), Branes in moduli spaces of Higgs bundles, II
• James Sparks (Oxford University), GK geometry
• Thomas Walpuski (Humboldt Universität zu Berlin), Problems with counting G2–instantons and associatives, and generalized Seiberg–Witten equations

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Arrival Date: Sunday January 5, 2020. Departure Date: Saturday January 11, 2020.

All talks will be at Huxley Bldg 140.  [ click for map ]

Registration and coffee/tea are in the Huxley 5th floor common room.

Scientific Organizers: Dominic Joyce joyce@maths.ox.ac.uk, Aleksander Doan doan@math.columbia.edu.

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Timetable

	MON 6 JAN	TUE 7 JAN	WED 8 JAN	THU 9 JAN	FRI 10 JAN
9:00 -9:30	REGISTRATION
9:30-10:30	Joyce	Donaldson 2	Doan	Georgieva	Li 2
10:30-11:00	Q&A / Discussion	Q&A / Discussion	Q&A / Discussion	Q&A / Discussion	Q&A / Discussion
11:00-11:30	Coffee	Coffee	Coffee	Coffee	Coffee
11:30-12:30	Thomas	Sun	Riviere	Ionel	He
12:30-14:00	Lunch	Lunch	Lunch	Lunch	Lunch
14:00-15:00	Pantev 1	Pantev 2	Maulik	Haydys
15:00-15:30	Coffee	Coffee	Coffee	Coffee
15:30-16:30	Donaldson 1	Safronov	Li 1	Shende
16:30-17:00	Q&A / Discussion	Q&A / Discussion	Q&A / Discussion	Q&A / Discussion
19:00-21:00			Social Dinner

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Speakers (click on title to see abstract and lecture slides):

• Aleksander Doan (Columbia and Cambridge), On complexification and categorification
• Sir Simon Donaldson (Simons Center, Stony Brook and Imperial College London), Gauge theory and special holonomy I,II
• Penka Georgieva (Jussieu), Real Gromov-Witten theory
• Andriy Haydys (Freiburg), On the blow up set for the Seiberg-Witten equations with two spinors
• Siqi He (Simons Center, Stony Brook), The counting problem of the Kapustin-Witten equations
• Eleny Ionel (Stanford), Counting embedded curves in 3-folds
• Dominic Joyce (Oxford), Shifted symplectic Derived Algebraic Geometry for dummies
• Yang Li (Institute for Advanced Study), Informal talk:
• Yang Li (Institute for Advanced Study), High codimension phenomena for Hermitian Yang-Mills connections
• Davesh Maulik (MIT), Stable pair invariants for Calabi-Yau 4-folds
• Tony Pantev (University of Pennsylvania), Constructing shifted symplectic structures
• Tristan Rivière (ETH, Zürich), L^p-bounded curvatures in high dimensions
• Pavel Safronov (Universität Zürich), Enumerative invariants from supersymmetric twists
• Vivek Shende (UC Berkeley), Skeins on Branes
• Song Sun (UC Berkeley), Singular Hermitian-Yang-Mills connections and reflexive sheaves
• Richard Thomas (Imperial College London), Borisov-Joyce in algebraic geometry

The workshop will have two main themes:

(A) The Donaldson-Segal programme for defining enumerative invariants of compact G2-manifolds by counting G2 instantons, with correction terms from associative 3-folds. Analysis of G2-instanton moduli spaces, singularities of G2-instantons. Analysis of Seiberg-Witten type equations on 3-manifolds used to define correction terms in Donaldson-Segal programme. Related gauge theory problems, including singularities of Hermitian-Yang Mills connections.

(B) The Pantev-Toën-Vaquié-Vezzosi theory of shifted symplectic derived algebraic geometry, giving geometric structures on Calabi-Yau moduli spaces, and its applications to generalizations of Donaldson-Thomas theory of Calabi-Yau 3- and 4-folds. One particular aim is to present the theory in a way accessible to String Theorists, to encourage communication between mathematicians and physicists on this subject, and to facilitate interpretation of the implications of the theory in String Theory terms. Algebro-geometric enumerative invariants (and Floer theories, etc), particularly of Calabi-Yau manifolds, related to the PTVV theory: Donaldson-Thomas, Gromov-Witten, and Vafa-Witten invariants, Donaldson-Thomas type invariants of Calabi-Yau 4-folds, the Gopakumar-Vafa conjecture.

Attendance at the workshop is by invitation only (except for London locals). Non-invitees wishing to attend may contact the organizers, but are likely to be disappointed, as we are already inviting as many as the lecture theatre will comfortably hold, so we can only include others if we have refusals.

Arrival date: Saturday, September 7.
Departure date: Wednesday afternoon, September 11, or Thursday, September 12.

Schedule:

	SUN 8 SEP	MON 9 SEP	TUES 10 SEP	WED 11 SEP
8:30 -9:30	Breakfast	Breakfast	Breakfast	Breakfast
9:30-10:30	B. Lawson	A. Hanany	C. Hull	C. Vafa
10:30-11:00	Coffee/tea	Coffee/tea	Coffee/tea	Coffee/tea
11:00-12:00	M. Larfors	R. Conlon	G. Ball	A. Klemm
12:00-13:00	Lunch	Lunch	Lunch	Lunch
13:00-14:00			D. Morrison (SCGP Weekly Talk)
13:30				Leave for NYC (from hotel)
14:00-15:00	S.-T. Yau	N. Fornasin
15:30-16:00	Tea	Tea	Tea
16:00-17:00	A. Waldron	B. Willett	A. Moroianu
18:00-20:00			Conference Banquet

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Speakers:

• Gavin Ball (Duke University), Quadratic closed G2-structures
• Ronan Conlon (Florida International University), Classification results for expanding and shrinking gradient Kähler-Ricci solitons
• Nelvis Fornasin (University of Freiburg), The eta invariant under cone-edge degeneration
• Amihay Hanany (Imperial College London), Hasse diagrams for symplectic singularities
• Chris Hull (Imperial College London), Special Holonomy Metrics, Degenerate Limits and Intersecting Branes
• Albrecht Klemm (University of Bonn), CY 3-folds over finite fields, Black hole attractors, and D-brane masses
• Magdalena Larfors (Uppsala University), Heterotic string theory and G2 structure manifolds
• Blaine Lawson (Stony Brook University), Pseudo-Convexity for the Special Lagrangian Potential Equation
• Andrei Moroianu (CNRS),  Toric nearly Kähler 6-manifolds
• David R. Morrison (UC Santa Barbara),  Nonaelian gauge symmetry and charged chiral matter in G_2 compactifications
• Cumrun Vafa (Harvard University), G2 Structure and Physical Interpretation of Taubes Construction of SW Invariants
• Alex Waldron (Michigan State University), G2-instantons on the 7-sphere
• Brian Willett (UC Santa Barbara), Global aspects of the 3d-3d correspondence
• Shing-Tung Yau (Harvard University), String duality and G₂ manifolds

This conference will be immediately followed by our Third annual meeting held at the Simons Foundation in New York City.